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Precise counting results for closed orbits of Anosov flows
 

Summary: Precise counting results for closed
orbits of Anosov flows
Nalini Anantharaman
Laboratoire de Probabilit´es (UMR 7599, CNRS)
Universit´e Paris 6
4, Place Jussieu
75252 Paris Cedex 05, France
ABSTRACT : We study the problem of counting closed geodesics according to their
lengths and under homological constraints on a compact surface of negative curvature.
We show how to use Dolgopyat's recent results to obtain a full asymptotic expansion, in
addition to the leading term given by Lalley.
We first state the properties of the stable and unstable leaves used by Chernov and
Dolgopyat; then we introduce the usual transfer operators and we prove the result with
the help of a dynamical -function.
RESUME : Nous ´etudions un probl`eme de d´enombrement de g´eod´esiques ferm´ees,
class´ees selon leur longueur et leur classe d'homologie, sur une surface compacte de cour-
bure n´egative. Nous expliquons comment les travaux r´ecents de Dolgopyat permettent de
donner un d´eveloppement asymptotique complet, en plus du terme principal d´ej`a obtenu
par Lalley.
Nous commen¸cons par ´enoncer les propri´et´es des feuilletages stable et instable utilis´ees

  

Source: Anantharaman, Nalini - Centre de Mathématiques Laurent Schwartz, École Polytechnique

 

Collections: Mathematics